Variation in number of days between full moons

So how long is it between one full moon and the next?

The typical answer is 29 and a half days.
However it can range between
29.8 days and 29.3 days.

More intrestingly the variation between the max and min number of days varies
from year to year. In some years the variation can be more than half a day,
in other years the diferance might be only a quater of a day.

For the real maths heads amongst you a spectral analysis gives two dominant
frequencies of 1/413 days and 1/362 days. I.E. with dominant frequency of once
every 413 days and beat frequency once every 7.92 years.